A method and corresponding apparatus for enhancing the capacity of communication and memory devices, said method comprising the representation of information by lattice points confined to a cubic region of an n-dimensional space, by means of which for example capacity gains of 50% or 100% and more may be achieved, relative to ‘conventional’ communication and storage methods.
Legal claims defining the scope of protection, as filed with the USPTO.
1. A method for encoding and decoding information on communication or memory devices, said method comprising: representing a bounded integer as a corresponding lattice point confined to a closed region of a multi-dimensional space having n dimensions; encoding said bounded integer into said device by setting said corresponding confined lattice point to a set of joint values of a characteristic physical variable; recovering said bounded integer from said device by: i) sensing said set of joint values of said characteristic physical variable; ii) detecting a corresponding confined lattice point from said set of sensed joint values; and iii) decoding said detected confined lattice point as a recovered bounded integer, wherein said lattice is represented by a triangular matrix.
2. A method according to claim 1 , wherein said lattice is brought to be represented by said triangular matrix.
3. A method according to claim 1 , wherein said lattice is a-priori represented by said triangular matrix.
4. A method according to claim 1 , wherein said triangular matrix comprises a generator matrix of said lattice.
5. A method according to claim 1 , wherein said triangular matrix comprises an inverse of the generator matrix of said lattice.
6. A method in accordance with claim 1 , wherein said confined lattice points are represented by a tree data structure, and all branches of any given layer of said tree are set to be of a same radix.
7. A method in accordance with claim 6 , wherein said radixes of said tree layers are pre-calculated.
8. A method in accordance with claim 7 , wherein said encoding comprises: converting said bounded integer into a corresponding radixes representation, and converting said corresponding radixes representation into said corresponding confined lattice point.
9. A method in accordance with claim 7 , wherein said decoding said detected confined lattice point as said recovered bounded integer comprises: converting said detected confined lattice point into a radixes representation; and converting said radixes representation into said recovered bounded integer.
10. A method in accordance with claim 1 , wherein said closed region is hyper-cubic.
11. A method in accordance with claim 1 , wherein said closed region is an n-polytope.
12. A method in accordance with claim 1 , wherein said closed region is hyper-spheric.
13. A method in accordance with claim 1 , wherein said closed region is hyper-ellipsoid.
14. A method in accordance with claim 1 , further comprising increasing the minimal distance between neighbor lattice points beyond the minimal distance achieved by lattice points contained in a closed region of a same volume and containing a same number of lattice points, said closed region being encoded by a cubic lattice, thus achieving an error probability gain.
15. A method in accordance with claim 1 , further comprising increasing the number of lattice points beyond the number of lattice points contained in a closed region of a same volume and encoded by a cubic lattice with same minimal distance, thus achieving density gain.
16. A method in accordance with claim 1 , further comprising increasing the minimal distance and the number of lattice points beyond those achieved by lattice points contained in a closed region of a same volume and encoded by a cubic lattice, thus achieving both error probability gain and density gain.
17. A method in accordance with claim 1 where said device comprises one of: a wireless communication device and a wired communication device.
18. A method in accordance with claim 1 , wherein said device comprises one of: a flash memory device, a semiconductor memory device, an optical media memory device, and a magnetic media memory device.
19. A method in accordance with claim 1 , wherein said lattice is E 8 .
20. A method in accordance with claim 1 , wherein said lattice is Λ 24 .
21. A method in accordance with claim 1 , wherein said lattice is one of: K 12 , Λ 16 , P 48 , N e64 , MW 80 , and MW 128 .
22. A method in accordance with claim 1 , where said lattice is any lattice.
23. A communication or memory device for encoding a bounded integer into a corresponding confined lattice point, comprising: arithmetic and logic operators operable to transform bounded integers into corresponding radix representations; and arithmetic and logic operators operable to transform, utilizing a triangular matrix, said radix representations into a confined lattice point or into an integer descriptor of said confined lattice point.
24. A communication or memory device in accordance with claim 23 , further comprising decoding a confined lattice point back into said corresponding bounded integer, comprising: arithmetic and logic operators operable to transform, utilizing said triangular matrix, a confined lattice point or confined lattice point integer descriptor into a radix representation; and arithmetic and logic operators operable to transform said radix representations into a bounded integer.
25. A communication or memory device in accordance with claim 23 further comprising: a memory element configured to store essential invention parameters comprising at least one of: a triangular matrix, a triangular generator matrix, a triangular inverse of said generator matrix, and a pre-calculated radix vector; and arithmetic and logic operators operable to sequence and control arithmetic and logic calculations.
26. A communication or memory device in accordance with claim 23 , wherein the radixes in said radix representation are mixed.
27. A communication or memory device in accordance with claim 23 , wherein the radixes in said radix representation are equal.
28. A communication or memory device in accordance with claim 23 , wherein said triangular matrix comprises a generator matrix of said lattice.
29. A communication or memory device in accordance with claim 23 , wherein said triangular matrix comprises an inverse generator matrix of said lattice.
Cooperative Patent Classification codes for this invention. Click any code to explore related patents in that topic.
August 5, 2010
November 6, 2012
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